Characteristics and Evolution of COVID-19 Cases in Brazil: Mathematical Modeling and Simulation

A critical review on applications of the Avrami equation beyond materials science

“…Though the JMAK model was developed to describe the progress of phase transformation in a material system, its application has not been limited to materials science. The model has been used in other fields of research, including life sciences examples such as oncology [35][36][37][38][39][40], ecology [41][42][43][44][45] and epidemiology [46][47][48][49][50]. Some systems from those contexts can be regarded as undergoing a 'phase transformation', and non-thermodynamic driving forces analogous to undercooling and supersaturation can be identified.…”

“…Notice that the n values for growth in plants and animals cluster around 2 (green shading) and the values for light-related processes cluster between 1 and 1. Augusto et al [47] used nucleation theory and the Avrami equation to model the fraction of population infected by COVID-19 in Brazil. They (tenuously) assume temperature to be equivalent to the 'degree' of people who are on the streets spreading the pandemic at the borders of contaminated neighbourhoods, without long-distance transmission.…”

“…Augusto et al . [ 47 ] used nucleation theory and the Avrami equation to model the fraction of population infected by COVID-19 in Brazil. They (tenuously) assume temperature to be equivalent to the ‘degree’ of people who are on the streets spreading the pandemic at the borders of contaminated neighbourhoods, without long-distance transmission.…”

“…This issue has been discussed previously [ 90 ] regarding application of the Avrami model in absorption processes [ 91 ]. The same issue is apparent in some epidemiology literature where the Avrami equation is used simply as a sigmoidal fit to COVID-19 pandemic data, without justification of the model parameters [ 47 – 50 ].…”